{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9af2c6c9",
   "metadata": {},
   "source": [
    "Chapter 7: Spatiotemporal Data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5ea4f83",
   "metadata": {},
   "source": [
    "Script 7-1: Analysis of Burkina Faso Market Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a38937f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "#import packages\n",
    "import igraph as ig\n",
    "from igraph import Graph\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import os\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0eae8082",
   "metadata": {},
   "outputs": [],
   "source": [
    "#import Burkina Faso market millet prices\n",
    "File=\"/Users/franckm/Documents/draftcodefiles/BF_Millet.csv\"\n",
    "pwd=os.getcwd()\n",
    "os.chdir(os.path.dirname(File))\n",
    "mydata=pd.read_csv(os.path.basename(File),encoding='latin1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a631cd7f",
   "metadata": {},
   "outputs": [],
   "source": [
    "#import weight matrix of Burkina Faso markets\n",
    "File=\"/Users/franckm/Documents/draftcodefiles/weights_bk.csv\"\n",
    "pwd=os.getcwd()\n",
    "os.chdir(os.path.dirname(File))\n",
    "weights=pd.read_csv(os.path.basename(File),encoding='latin1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7d29310a",
   "metadata": {},
   "outputs": [],
   "source": [
    "#score in yearly sets with 3 quarter overlap\n",
    "vcurv_t=[]\n",
    "vcurv_ave=[]\n",
    "eig_t=[]\n",
    "eig_ave=[]\n",
    "nets=[]\n",
    "for Year in range(4,29):\n",
    "    data=mydata.iloc[(Year-4):(Year),1:46]\n",
    "    cor=np.corrcoef(data.transpose())\n",
    "    weights_total=weights.iloc[:,1:46]\n",
    "    cor[cor>=0.9]=1\n",
    "    cor[cor<0.9]=0\n",
    "    cor_weighted=np.multiply(cor,weights_total)\n",
    "    bf_market_w=Graph.Adjacency(cor_weighted,diag=False)\n",
    "    edge_list=bf_market_w.get_edgelist()\n",
    "    self_loop=[]\n",
    "    for i in range(0,46):\n",
    "        self=(i,i)\n",
    "        self_loop.append(self)\n",
    "    to_remove=[]\n",
    "    for i in edge_list:\n",
    "        for j in self_loop:\n",
    "            if i==j:\n",
    "                to_remove.append(i)\n",
    "    bf_market_w.delete_edges(to_remove)\n",
    "    nets.append(bf_market_w)\n",
    "    d=Graph.degree(bf_market_w)\n",
    "    e=Graph.pagerank(bf_market_w)\n",
    "    eig_t.append(e)\n",
    "    eig_ave.append(np.mean(e))\n",
    "    ecurvw=[]\n",
    "    for edge in bf_market_w.es:\n",
    "        s=edge.source\n",
    "        t=edge.target\n",
    "        ecurvw.append(2-d[s]-d[t])\n",
    "    vcurvw=[]\n",
    "    for vertex in bf_market_w.vs:\n",
    "        inc=Graph.incident(bf_market_w,vertex)\n",
    "        inc_curv=[]\n",
    "        for i in inc:\n",
    "            inc_curv.append(ecurvw[i])\n",
    "        vcurvw.append(sum(inc_curv))\n",
    "    vcurv_t.append(vcurvw)\n",
    "    vcurv_ave.append(np.mean(vcurv_t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b9d290a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot metric averages across time slices\n",
    "time=range(0,25)\n",
    "plt.plot(time, eig_ave, label = \"Pagerank Average\")\n",
    "plt.plot(time, vcurv_ave, label = \"Forman-Ricci Curvature Avereage\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "78d1b718",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"600pt\" height=\"600pt\" viewBox=\"0 0 600 600\" version=\"1.1\">\n",
       "<g id=\"surface2\">\n",
       "<rect x=\"0\" y=\"0\" width=\"600\" height=\"600\" style=\"fill:rgb(100%,100%,100%);fill-opacity:1;stroke:none;\"/>\n",
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       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<igraph.drawing.cairo.plot.CairoPlot at 0x7ff0743e47f0>"
      ]
     },
     "execution_count": 7,
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#examine different time points with Forman-Ricci curvature plots, fourth slice\n",
    "ig.plot(nets[4],vertex_size=np.array(vcurv_t[4])*-0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "56630e53",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<igraph.drawing.cairo.plot.CairoPlot at 0x7ff0747b7340>"
      ]
     },
     "execution_count": 8,
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#examine different time points with Forman-Ricci curvature plots, 19th slice\n",
    "ig.plot(nets[19],vertex_size=np.array(vcurv_t[19])*-0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bdfa0427",
   "metadata": {},
   "source": [
    "Script 7-2: Store Sales Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b06e28d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "#import Store Sales dataset\n",
    "File=\"C:/users/njfar/OneDrive/Desktop/Store_Sales.csv\"\n",
    "\n",
    "pwd=os.getcwd()\n",
    "os.chdir(os.path.dirname(File))\n",
    "mydata=pd.read_csv(os.path.basename(File),encoding='latin1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2457e4cb",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\njfar\\anaconda3\\lib\\site-packages\\numpy\\lib\\function_base.py:2691: RuntimeWarning: invalid value encountered in true_divide\n",
      "  c /= stddev[:, None]\n",
      "C:\\Users\\njfar\\anaconda3\\lib\\site-packages\\numpy\\lib\\function_base.py:2692: RuntimeWarning: invalid value encountered in true_divide\n",
      "  c /= stddev[None, :]\n"
     ]
    }
   ],
   "source": [
    "#score in yearly sets with 3 quarter overlap\n",
    "vcurv_t=[]\n",
    "vcurv_ave=[]\n",
    "eig_t=[]\n",
    "eig_ave=[]\n",
    "nets=[]\n",
    "for Month in range(2,54):\n",
    "    data=mydata.iloc[(Month-2):(Month),1:6]\n",
    "    cor=np.corrcoef(data.transpose())\n",
    "    cor[cor>=0.9]=1\n",
    "    cor[cor<0.9]=0\n",
    "    stores=Graph.Adjacency(cor,diag=False)\n",
    "    edge_list=stores.get_edgelist()\n",
    "    self_loop=[]\n",
    "    for i in range(0,46):\n",
    "        self=(i,i)\n",
    "        self_loop.append(self)\n",
    "    to_remove=[]\n",
    "    for i in edge_list:\n",
    "        for j in self_loop:\n",
    "            if i==j:\n",
    "                to_remove.append(i)\n",
    "    stores.delete_edges(to_remove)\n",
    "    nets.append(stores)\n",
    "    d=Graph.degree(stores)\n",
    "    e=Graph.pagerank(stores)\n",
    "    eig_t.append(e)\n",
    "    eig_ave.append(np.mean(e))\n",
    "    ecurvw=[]\n",
    "    for edge in stores.es:\n",
    "        s=edge.source\n",
    "        t=edge.target\n",
    "        ecurvw.append(2-d[s]-d[t])\n",
    "    vcurvw=[]\n",
    "    for vertex in stores.vs:\n",
    "        inc=Graph.incident(stores,vertex)\n",
    "        inc_curv=[]\n",
    "        for i in inc:\n",
    "            inc_curv.append(ecurvw[i])\n",
    "        vcurvw.append(sum(inc_curv))\n",
    "    vcurv_t.append(vcurvw)\n",
    "    vcurv_ave.append(np.mean(vcurv_t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "fd421ef6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot metric averages across time slices\n",
    "time=range(0,52)\n",
    "plt.plot(time, eig_ave, label = \"Pagerank Average\")\n",
    "plt.plot(time, vcurv_ave, label = \"Forman-Ricci Curvature Avereage\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "39b145ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"600\" height=\"600\" viewBox=\"0 0 600 600\">\n",
       "<rect x=\"-60\" y=\"-60\" width=\"720\" height=\"720\" fill=\"rgb(100%, 100%, 100%)\" fill-opacity=\"1\"/>\n",
       "<path fill=\"none\" stroke-width=\"1\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke=\"rgb(26.666667%, 26.666667%, 26.666667%)\" stroke-opacity=\"1\" stroke-miterlimit=\"10\" d=\"M 580 361.359375 C 502.296875 411.804688 443.863281 523.253906 503.453125 570.105469 \"/>\n",
       "<path fill-rule=\"nonzero\" fill=\"rgb(26.666667%, 26.666667%, 26.666667%)\" fill-opacity=\"1\" d=\"M 514.667969 578.921875 L 500.585938 573.746094 L 506.316406 566.460938 L 514.667969 578.921875 \"/>\n",
       "<path fill=\"none\" stroke-width=\"1\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke=\"rgb(26.666667%, 26.666667%, 26.666667%)\" stroke-opacity=\"1\" stroke-miterlimit=\"10\" d=\"M 515.066406 579.234375 C 589.394531 528.734375 615.820312 459.609375 585.058594 375.238281 \"/>\n",
       "<path fill-rule=\"nonzero\" fill=\"rgb(26.666667%, 26.666667%, 26.666667%)\" fill-opacity=\"1\" d=\"M 580.171875 361.835938 L 589.414062 373.648438 L 580.707031 376.824219 L 580.171875 361.835938 \"/>\n",
       "<path fill=\"none\" stroke-width=\"1\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke=\"rgb(0%, 0%, 0%)\" stroke-opacity=\"1\" stroke-miterlimit=\"10\" d=\"M 186.898438 20 L 186.898438 20 \"/>\n",
       "<path fill-rule=\"nonzero\" fill=\"rgb(100%, 0%, 0%)\" fill-opacity=\"1\" stroke-width=\"1\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke=\"rgb(0%, 0%, 0%)\" stroke-opacity=\"1\" stroke-miterlimit=\"10\" d=\"M 580.5 361.359375 C 580.5 362.023438 579.5 362.023438 579.5 361.359375 C 579.5 360.691406 580.5 360.691406 580.5 361.359375 \"/>\n",
       "<path fill-rule=\"nonzero\" fill=\"rgb(100%, 0%, 0%)\" fill-opacity=\"1\" stroke-width=\"1\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke=\"rgb(0%, 0%, 0%)\" stroke-opacity=\"1\" stroke-miterlimit=\"10\" d=\"M 515.566406 579.234375 C 515.566406 579.902344 514.566406 579.902344 514.566406 579.234375 C 514.566406 578.566406 515.566406 578.566406 515.566406 579.234375 \"/>\n",
       "<path fill=\"none\" stroke-width=\"1\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke=\"rgb(0%, 0%, 0%)\" stroke-opacity=\"1\" stroke-miterlimit=\"10\" d=\"M 20 580 L 20 580 \"/>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<igraph.drawing.cairo.plot.CairoPlot at 0x22833329df0>"
      ]
     },
     "execution_count": 11,
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#examine different time points with Forman-Ricci curvature plots, tenth slice\n",
    "ig.plot(nets[10],vertex_size=np.array(vcurv_t[10])*-0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "522753d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"600\" height=\"600\" viewBox=\"0 0 600 600\">\n",
       "<rect x=\"-60\" y=\"-60\" width=\"720\" height=\"720\" fill=\"rgb(100%, 100%, 100%)\" fill-opacity=\"1\"/>\n",
       "<path fill=\"none\" stroke-width=\"1\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke=\"rgb(26.666667%, 26.666667%, 26.666667%)\" stroke-opacity=\"1\" stroke-miterlimit=\"10\" d=\"M 580 425.015625 C 415.378906 374.753906 316.488281 456.722656 191.550781 565.570312 \"/>\n",
       "<path fill-rule=\"nonzero\" fill=\"rgb(26.666667%, 26.666667%, 26.666667%)\" fill-opacity=\"1\" d=\"M 180.792969 574.941406 L 188.503906 562.074219 L 194.59375 569.0625 L 180.792969 574.941406 \"/>\n",
       "<path fill=\"none\" stroke-width=\"1\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke=\"rgb(26.666667%, 26.666667%, 26.666667%)\" stroke-opacity=\"1\" stroke-miterlimit=\"10\" d=\"M 580 425.015625 C 464.199219 205.503906 284.09375 117.703125 41.566406 170.308594 \"/>\n",
       "<path fill-rule=\"nonzero\" fill=\"rgb(26.666667%, 26.666667%, 26.666667%)\" fill-opacity=\"1\" d=\"M 27.625 173.332031 L 40.585938 165.777344 L 42.550781 174.839844 L 27.625 173.332031 \"/>\n",
       "<path fill=\"none\" stroke-width=\"1\" stroke-linecap=\"butt\" stroke-linejoin=\"miter\" stroke=\"rgb(26.666667%, 26.666667%, 26.666667%)\" stroke-opacity=\"1\" stroke-miterlimit=\"10\" d=\"M 580 425.015625 C 632.785156 259.785156 589.542969 125.132812 443.421875 31.761719 \"/>\n",
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      ],
      "text/plain": [
       "<igraph.drawing.cairo.plot.CairoPlot at 0x228333294c0>"
      ]
     },
     "execution_count": 12,
     "metadata": {
      "image/svg+xml": {
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      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#examine different time points with Forman-Ricci curvature plots, thirtieth slice\n",
    "ig.plot(nets[30],vertex_size=np.array(vcurv_t[30])*-0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8f47d678",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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